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A204039 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.

%I A204039 #7 Jul 22 2025 17:43:45
%S A204039 16,44,44,121,164,121,286,603,603,286,676,1758,2928,1758,676,1482,
%T A204039 5130,10505,10505,5130,1482,3249,13040,37642,44366,37642,13040,3249,
%U A204039 6840,33223,111578,189580,189580,111578,33223,6840,14400,77574,330509,642272
%N A204039 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards.
%C A204039 Table starts
%C A204039 ...16....44....121.....286......676......1482.......3249.......6840.......14400
%C A204039 ...44...164....603....1758.....5130.....13040......33223......77574......181559
%C A204039 ..121...603...2928...10505....37642....111578.....330509.....863435.....2254026
%C A204039 ..286..1758..10505...44366...189580....642272....2198077....6415866....18855400
%C A204039 ..676..5130..37642..189580...969528...3811097...15164049...50226272...167435933
%C A204039 .1482.13040.111578..642272..3811097..16895850...76619720..282617310..1055589853
%C A204039 .3249.33223.330509.2198077.15164049..76619720..397550036.1650280817..6940548943
%C A204039 .6840.77574.863435.6415866.50226272.282617310.1650280817.7576693894.35441648714
%H A204039 R. H. Hardin, <a href="/A204039/b204039.txt">Table of n, a(n) for n = 1..364</a>
%e A204039 Some solutions for n=4 k=3
%e A204039 ..1..0..1..1....1..0..0..1....0..1..0..1....0..1..1..0....1..0..0..0
%e A204039 ..0..1..1..0....0..0..1..0....1..0..1..0....1..0..0..1....0..1..1..1
%e A204039 ..1..0..1..1....1..1..0..1....0..1..1..1....0..1..1..1....1..0..1..1
%e A204039 ..0..1..1..1....0..1..1..1....1..0..1..1....0..1..1..1....1..1..1..1
%e A204039 ..0..1..1..1....1..1..0..1....0..1..1..1....0..1..1..1....1..1..1..1
%K A204039 nonn,tabl
%O A204039 1,1
%A A204039 _R. H. Hardin_ Jan 09 2012